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Cars Analysis
Alejandro Fernandez Benages
17/03/2021
1. EDA
1.1 Knowing the data
To list the attributes of the data set.
attributes(cars)## $names
## [1] "speed" "dist"
##
## $class
## [1] "data.frame"
##
## $row.names
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50To print the min, max, mean, median, and quartiles of each attribute.
summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00To display the structure of your data set.
str(cars) ## 'data.frame': 50 obs. of 2 variables:
## $ speed: num 4 4 7 7 8 9 10 10 10 11 ...
## $ dist : num 2 10 4 22 16 10 18 26 34 17 ...To get th names of the attributes within your data set.
names(cars) ## [1] "speed" "dist"1.2 Some Plotting . The most frequent speed of cars is between 10 to 20.
hist(cars$speed,
main="Speed distribution", xlab="Speed [mph]")
The most frequent distance of most cars is between 20 to 40.
hist(cars$dist,
main="Stopping distance distribution", xlab="Stopping Distance [feet]")
Normal Quantile Plot is a way to see if your data is normally distributed. We can see that there is a positive correlation btw Speed and Distance
qqnorm(cars$speed)
qqnorm(cars$dist)
plot(cars, col='blue', pch=20, cex=2,
main="Speed and Stopping Distance for 50 Cars",
xlab="Speed [mph]", ylab="Stopping Distance [feet]")
Missing Values? Will count how many NA’s you have.
summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00Will show your NA’s through logical data. (TRUE if it’s missing, FALSE if it’s not.)
is.na(cars) ## speed dist
## [1,] FALSE FALSE
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## [50,] FALSE FALSEReplace the missing values with the mean, which is common technique, but something to use with care with as it can skew the data.
#DatasetName$ColumnName[is.na(DatasetName$ColumnName)]<-mean(DatasetName$ColumnName,na.rm = TRUE)Creating Testing and Training Sets
set.seed(122)
# These two lines calculate the sizes of each set but do not create the sets:
trainSize<-round(nrow(cars)*0.7) # 70/30%
testSize<-nrow(cars)-trainSize
# If you’d like to see how many instances will be in each set..
trainSize## [1] 35testSize## [1] 15# How do you create the train/test sets?. We also want these sets to be in a randomized order, which will create the most optimal model.
# To perform this, you need to run these three lines of code.
training_indices<-sample(seq_len(nrow(cars)),size =trainSize)
trainSet<-cars[training_indices,]
testSet<-cars[-training_indices,]
# Linear Regression
# *****************
# The basic line of code for the linear model function.
cars_regression <-lm(formula = dist~ speed, trainSet)
# To see key metrics of your model:
summary(cars_regression)##
## Call:
## lm(formula = dist ~ speed, data = trainSet)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26.565 -10.236 -2.565 9.379 42.929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -13.082 8.563 -1.528 0.136
## speed 3.582 0.506 7.080 4.18e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.75 on 33 degrees of freedom
## Multiple R-squared: 0.603, Adjusted R-squared: 0.591
## F-statistic: 50.13 on 1 and 33 DF, p-value: 4.181e-08Predictions
cars_predictions <- predict(cars_regression, testSet)
cars_predictions## 1 3 8 11 14 16 17 18
## 1.247655 11.994691 22.741727 26.324072 29.906418 33.488763 33.488763 33.488763
## 20 22 30 32 33 38 49
## 37.071108 37.071108 47.818144 51.400490 51.400490 54.982835 72.894561Confidence in your predictions: In order to have an idea about the accuracy of the predictions, you can ask for intervals around your prediction. To get a matrix with the prediction and a 95 percent confidence interval around the mean prediction, you set the argument interval to ‘confidence’ like this:
predict(cars_regression,trainSet, interval='confidence')## fit lwr upr
## 48 72.894561 63.111447 82.67768
## 40 58.565180 51.814724 65.31564
## 9 22.741727 14.460418 31.02304
## 47 72.894561 63.111447 82.67768
## 44 65.729871 57.581248 73.87849
## 41 58.565180 51.814724 65.31564
## 34 51.400490 45.637230 57.16375
## 19 33.488763 27.210054 39.76747
## 31 47.818144 42.321088 53.31520
## 37 54.982835 48.791536 61.17413
## 10 26.324072 18.791390 33.85676
## 45 69.312216 60.368226 78.25621
## 12 29.906418 23.049158 36.76368
## 6 19.159382 10.074322 28.24444
## 39 58.565180 51.814724 65.31564
## 36 54.982835 48.791536 61.17413
## 4 11.994691 1.186675 22.80271
## 7 22.741727 14.460418 31.02304
## 2 1.247655 -12.321487 14.81680
## 46 72.894561 63.111447 82.67768
## 23 37.071108 31.245146 42.89707
## 42 58.565180 51.814724 65.31564
## 28 44.235799 38.819199 49.65240
## 21 37.071108 31.245146 42.89707
## 35 51.400490 45.637230 57.16375
## 25 40.653454 35.123448 46.18346
## 43 58.565180 51.814724 65.31564
## 24 40.653454 35.123448 46.18346
## 27 44.235799 38.819199 49.65240
## 26 40.653454 35.123448 46.18346
## 13 29.906418 23.049158 36.76368
## 15 29.906418 23.049158 36.76368
## 5 15.577037 5.646476 25.50760
## 29 47.818144 42.321088 53.31520
## 50 76.476907 65.821243 87.13257predict(cars_regression,testSet, interval='prediction')## fit lwr upr
## 1 1.247655 -33.547942 36.04325
## 3 11.994691 -21.819880 45.80926
## 8 22.741727 -10.351959 55.83541
## 11 26.324072 -6.590260 59.23841
## 14 29.906418 -2.859937 62.67277
## 16 33.488763 0.838584 66.13894
## 17 33.488763 0.838584 66.13894
## 18 33.488763 0.838584 66.13894
## 20 37.071108 4.504963 69.63725
## 22 37.071108 4.504963 69.63725
## 30 47.818144 15.309228 80.32706
## 32 51.400490 18.845503 83.95548
## 33 51.400490 18.845503 83.95548
## 38 54.982835 22.349352 87.61632
## 49 72.894561 39.393497 106.39563# rmarkdown::render("cars.html")